Large deviations for integer centered Poisson approximation (Q1567711)

Let \(X\) be a nonnegative integer-valued random variable, whose factorial cumulants \(\Gamma_k\), \(k\geq 2\), are such that \(|\Gamma_k|\leq k!\lambda/\Delta^{k-1}\) for some \(\Delta\geq 1\). The main results of the paper are Cramér type approximations to the tails of the distribution of \(X\), in terms of corrections to a centred Poisson approximation. The proofs use conjugate distributions and the saddle point method for Fourier inversion.